Best Known (43−10, 43, s)-Nets in Base 9
(43−10, 43, 11811)-Net over F9 — Constructive and digital
Digital (33, 43, 11811)-net over F9, using
- 91 times duplication [i] based on digital (32, 42, 11811)-net over F9, using
- net defined by OOA [i] based on linear OOA(942, 11811, F9, 10, 10) (dual of [(11811, 10), 118068, 11]-NRT-code), using
- OA 5-folding and stacking [i] based on linear OA(942, 59055, F9, 10) (dual of [59055, 59013, 11]-code), using
- construction X applied to Ce(9) ⊂ Ce(7) [i] based on
- linear OA(941, 59049, F9, 10) (dual of [59049, 59008, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(936, 59049, F9, 8) (dual of [59049, 59013, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(91, 6, F9, 1) (dual of [6, 5, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(91, s, F9, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(9) ⊂ Ce(7) [i] based on
- OA 5-folding and stacking [i] based on linear OA(942, 59055, F9, 10) (dual of [59055, 59013, 11]-code), using
- net defined by OOA [i] based on linear OOA(942, 11811, F9, 10, 10) (dual of [(11811, 10), 118068, 11]-NRT-code), using
(43−10, 43, 48121)-Net over F9 — Digital
Digital (33, 43, 48121)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(943, 48121, F9, 10) (dual of [48121, 48078, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(943, 59059, F9, 10) (dual of [59059, 59016, 11]-code), using
- construction X applied to Ce(9) ⊂ Ce(6) [i] based on
- linear OA(941, 59049, F9, 10) (dual of [59049, 59008, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(931, 59049, F9, 7) (dual of [59049, 59018, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(92, 10, F9, 2) (dual of [10, 8, 3]-code or 10-arc in PG(1,9)), using
- extended Reed–Solomon code RSe(8,9) [i]
- Hamming code H(2,9) [i]
- construction X applied to Ce(9) ⊂ Ce(6) [i] based on
- discarding factors / shortening the dual code based on linear OA(943, 59059, F9, 10) (dual of [59059, 59016, 11]-code), using
(43−10, 43, large)-Net in Base 9 — Upper bound on s
There is no (33, 43, large)-net in base 9, because
- 8 times m-reduction [i] would yield (33, 35, large)-net in base 9, but